Question : A sum of Rs. 600 becomes Rs. 840 at simple interest in 4 years. In how many years will the sum of Rs. 1500 amount to Rs. 2100 at the same rate of simple interest?
Option 1: 5 years
Option 2: 4 years
Option 3: 2 years
Option 4: 3 years
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Correct Answer: 4 years
Solution : Given, P = Rs. 600, A = Rs. 840, and T = 4 years, Simple interest, SI = Amount – Principal we can find the rate of interest (R): ⇒ R = $\frac{SI×100}{P×T}$ ⇒ R = $\frac{840−600}{600×4}×100$ ⇒ R = $\frac{240}{2400}×100$ ⇒ R = 10% Now, we can use this rate of interest to find the time (T′) for the new principal (P′) and amount (A′). A′ = P′ + SI′ and SI′ = P′ × R × T′ Given, P′ = Rs.1500 and A′ = Rs. 2100 Let the time be T'. And, T′= $\frac{SI'×100}{P′ × R}$ ⇒ T′ = $\frac{2100−1500}{1500×10}×100$ ⇒ T′ = $\frac{600}{15000}×100$ ⇒ T′ = 4 years Hence, the correct answer is 4 years.
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